What is the integral of (e^{5sqrt(t)})/(sqrt(t)) ?

The integral of (e^{5sqrt(t)})/(sqrt(t)) is 2/5 e^{5sqrt(t)}+C

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integral of (e^{5sqrt(t)})/(sqrt(t))

\int \frac{e ^{5 t}}{t} d t

\frac{2}{5} e^{5 t} + C

Solution steps

\int \frac{e ^{5 t}}{t} d t

Apply u-substitution

: \int \frac{2 e ^{u}}{5} d u

= \int \frac{2 e ^{u}}{5} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{2}{5} \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= \frac{2}{5} e^{u}

Substitute back

u = 5 t

= \frac{2}{5} e^{5 t}

Add a constant to the solution

= \frac{2}{5} e^{5 t} + C

\frac{d ^{2} y}{d x ^{2}} + 64 y = 0

\frac{\partial}{\partial x} (1 - x^{7} - y^{7})

θ \to 0 lim (sin (θ) ln (θ))

f (x) = \frac{x ^{2} - 1}{x}

\frac{d}{d x} (1 5^{x})

What is the integral of (e^{5sqrt(t)})/(sqrt(t)) ?
The integral of (e^{5sqrt(t)})/(sqrt(t)) is 2/5 e^{5sqrt(t)}+C